Factor completely.
$x^2-40x+400$

• A. $(x-20)(x+20)$
• B. $(x-4)(x-100)$
• C. ${(x-20)}^2$
• D. $(x-4)(x+100)$

Answer: (C)

Verified step by step guidance

1. Identify the general form of a perfect square trinomial, which is either \(a^{2} + 2ab + b^{2}\) or \(a^{2} - 2ab + b^{2}\). These factor into \((a + b)^{2}\) or \((a - b)^{2}\) respectively.
2. Look at the given trinomial and determine if it fits the pattern of a perfect square trinomial by checking if the first and last terms are perfect squares and if the middle term is twice the product of the square roots of the first and last terms.
3. Express the first and last terms as squares, for example, write \(x^{2}\) as \((x)^{2}\) and \$9\( as \)(3)^{2}$.
4. Check if the middle term matches \$2ab\( or \)-2ab\( where \)a\( and \)b$ are the square roots found in the previous step. This confirms the trinomial is a perfect square.
5. Write the factorization of the trinomial as \((a + b)^{2}\) or \((a - b)^{2}\) depending on the sign of the middle term.